In information theory, a low-density parity-check (LDPC) code is a linear error correcting code and a method of transmitting a message over a noisy transmission channel and is constructed using a sparse bipartite graph. LDPC codes are capacity-approaching codes, which means that practical constructions exist that allow a noise threshold to be set very close to a theoretical maximum for a symmetric memory-less channel. The noise threshold defines an upper bound for the channel noise, up to which the probability of lost information can be made as small as desired. Using iterative belief propagation techniques, LDPC codes can be decoded in time linear to their block length.
U.S. Pat. No. 6,715,121 discloses a process for the construction of LDPC codes including N symbols, can adapt to non-binary codes, of which K are free, each code being defined by a check matrix A including M=N−K rows, N columns, and t nonzero symbols in each column. The method includes allocating the same number of nonzero symbols to all rows of the check matrix A, taking t to be the smallest possible odd number, defining the columns of A such that any two columns of the check matrix A have at most one nonzero value in a common position, and defining the rows of A such that any two rows of the check matrix A have only one nonzero value in a common position.
However, the process for the construction of LDPC codes adapting to non-binary codes has high decoding complexity and is accomplished with difficulty in hardware.
Accordingly, a new decoding device for non-binary QC-LDPC codes and associated method that has low decoding complexity and is accomplished easily in hardware are needed to overcome the foregoing problems.